Annals of Combinatorics

, Volume 9, Issue 2, pp 205–221

The q-Markov-WZ Method

Authors

    • Department of MathematicsRutgers University (New Brunswick)
Original Paper

DOI: 10.1007/s00026-005-0252-8

Cite this article as:
Mohammed, M. Ann. Comb. (2005) 9: 205. doi:10.1007/s00026-005-0252-8

Abstract.

Andrei Markov’s 1890 beautiful ad-hoc method of transforming a series of hypergeometric type into a rapidly-converging series was upgraded recently to a full-fledged method by Mohammed and Zeilberger, but only for the ordinary case. In this article, the q-case is developed and it is shown how Markov’s ad-hoc method, when coupled with q-WZ theory and q-Gosper’s algorithm, leads to a new class of identities and very fast convergence-acceleration series that can be applied to any infinite series of q-hypergeometric type.

AMS Subject Classification.

05A10 05A19 33F10 33C20 33-04

Keywords.

WZ theory series convergence q-hypergeometric q-Gosper’s algorithm q-Zeilberger’s algorithm

Copyright information

© Birkhäuser Verlag, Basel 2005